Common and Coincidence Fixed-Point Theorems for <i>ℑ</i>-Contractions with Existence Results for Nonlinear Fractional Differential Equations

Abstract

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.

Keywords

• common fixed point
• generalized metric space
• coincidence fixed point
• <i>ℑ</i>-contraction
• fractional differential equation
• integral boundary conditions